Coherently photo-induced ferromagnetism
in diluted magnetic semiconductors
J. Fernandez-Rossier (University of Alicante, UT), C. Piermarocchi (MS), P. Chen (UCB), L. J. Sham (UCSD), A.H. MacDonald (UT)
Paramagnetic semiconductor (II,Mn)VI can become ferromagnetic when illuminated by coherent unpolarized light of frequency below the semiconductor band-gap.
EGEF
Properties of the Diluted paramagnetic (II(1-x),Mnx)-VI
(II(1-x),Mnx)-VI(Zn(1-x),Mnx)-Se(Zn(1-x),Mnx)-S (Cd(1-x),Mnx)-Te
Mn-Mn interaction: only first neighbors. For x=0.012 • 0.002 coupled to nn (2%)•0.01 is free (80%) -PARAMAGNET
If doped with holes, FERROMAGNET at Tc<2 Kelvin
Laser features:
• Frequency below gap: =EG-L>0• No Photocarriers, no doping
• Intensity (=dcvE0>0.1 meV)
• Polarization state: not relevant
Coherently photo-induced ferromagnetism
This prediction is a logical consequence of:•Experimentally established facts•Theoretical concepts in agreement with experiments
<M>=0
Exchange Interaction. Giant Spin Splitting Selection Rules
L
jsdcMn<M>
jpdcMn<M>
B
Macroscopic Explanation of optical ferromagnetism
EEU L'
Reactive optical energy, due to matter-laser interaction:
MMU
22
•U depends on <M>: U(M)•Ferromagnetism (<M>0) minimizes U (M)•But entropy favours <M>=0
Competition between reactive optical energy and entropy
Electric Field of the Laser
Real part of retarded Optical Response function
MTSkMUTMG B
,
Entropic PenaltyParamagnetic Gain
(Optical Energy)
Functional of Carrier Density Matrix
What is the density matrix of the laser driven (II,Mn)-VI semiconductor?
Density matrix: effect of the laser
L
k
kkH
2
1
Rotating FrameRWA
kU
kL
kE
EH
0
0
2
1
EU(k)
EL(k)
> >(T1)-
1
BBeeH titi LL int
BBeH ti L 2int 1
00
01
2
2
vuv
uvu Coherent
Occupation
0'' L
No absorption= No real carriers
eff= -|J|>0
2
McJJMJ Mneh
Interaction “Bosonic Model”
Laser Matter Linear response (*)
h-Mn, e-Mn MF VCA
Electron-Hole All orders
e-e and h-h Irrelevant (linear response)
Microscopic Theory: Relevant Interactions
•(*) Linear Response: Good if >•OK, since >|J|> and |J|>20 meV
BBgBBMJH
02 1s
Vg
2
McJJMJ Mneh
MJMJMU
V s 11
)0(2
,,1 2
1
2
Microscopic Theory: Bosonic Model
0 1 2M
-1.45
-1.44
-1.43
-1.42
G (
10-2
meV
nm
-3)
(b)
-0.4
-0.2
0S
(10
-2 m
eV n
m-3)
T=115 mKT=105 mK
(a)
-2 -1 0 1 2M
-1.2
-1
U (
10-2
meV
nm-3
)
0 0.5 1T /TC
0
1
2
M
=26 meV, TC=780 mK
=41 meV, TC=114 mK
=71 meV, TC=22 mK
Results for (Zn0.988,Mn0.012) S
1.50
1.00
0.50
Transition Temperature for (Zn0.988,Mn0.012) S
•Tc2
•Tc -3
Linear response fails there
Isothermal transitions for (Zn,Mn) S
T=0.5 K
Switching ferromagnetism
on and off!!!
Materials and Lasers
Important material properties:•Robust Excitons•Not much Mn (x=1%)•(Zn,Mn)S, (Zn,Mn)Se•(Zn,Mn)O ??
Laser properties:•Tunable, around material band-gap•Intense lasers•Tc <50 mK with cw laser•Pulse duration longer thanSwitching time•Switching time: interesting question !!!!
ORKKY vs coherently photo-induced FM
jpd jpd
jpd
jsd
jsd jsd
2121 )( SSRRJH
2
13
22 )0(
3
1sMnpdsdc cJJ
SST
The SAME than Bosonic Model
(*) C. Piermarocchi, P. Chen, L.J. Sham and D. G. SteelPRL89 , 167402 (2002)
Conclusions
•New way of making semiconductors ferromagnetic•Ferromagnetism mediated by virtual carriers•Originated by optical coherence•Possible at T>1 Kelvin (with the right laser)
Phase DiagramAlways
absorbing T
(/J)
Absorbing FM
Coherent PM
Always coherent
PM
PM
FMFM
T=1.5 KT=2.0
K
Interaction ‘BCS’ “Bosonic Model”
Laser Matter All orders Linear response (*)
h-Mn, e-Mn MF VCA MF VCA
Electron-Hole Pairing All orders
Mn-Mn AF s-exc x replaced by xeff x replaced by xeff
e-e and h-h Hartree-Fock Irrelevant (linear response)
Microscopic Theory: Relevant Interactions
* Linear Response: Good if >
No absorption= No real carriers= Optical Coherence:
eff= -|J|>0, where 2
McJJMJ Mneh
Carrier mediated ferromagnetism
MTSkMETMG Bcarrier
,
Entropic Penalty
Paramagneticgain
MSJMEMEcarrier
0
Functional of carrier density matrix
What is the density matrix of the laser driven (II,Mn)-VI semiconductor?
B C
Al Si
N O
P S
Ga Ge
In Sn
As Se
Sb
II
Zn
Cd
Hg
IV VIII VI
Te
EGEF
II-VIZn-SeZn-S Cd-Te
II
B C
Al Si
N O
P S
Ga Ge
In Sn
As Se
Sb
IV VIII VI
Te
Zn
Cd
Hg
Mn
EGEF
Diluted paramagnetic semiconductor
(II,Mn)-VI(Zn,Mn)-Se(Zn,Mn)-S (Cd,Mn)-Te
Laser features:
• Frequency below gap: =EG-L>0• No Photocarriers
• Intense (=dcvE0>0.1 meV)
• Non circularly polarized
Coherently photo-induced ferromagnetism
II
B C
Al Si
N O
P S
Ga Ge
In Sn
As Se
Sb
IV VIII VI
Te
Zn
Cd
Hg
Mn
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